Sounds impractical to me. In fact every company I've worked for is flooded with non-Americans. It would be tough to find a company that only hires Americans.
I think a better solution is to end H-1B. Nobody is forcing people to come here.
That's the whole point, that's why H1B is apparently still very popular. People will take lower salaries just to get to the US because they apparently want to move there at all cost and have a chance to stay.